We prove that for every integer n, there exist infinitely many D(n)-triples which are also D(t)-triples for t∈ Z with n≠ t. We also prove that there are infinitely many D(- 1) -triples in Z[i] which are also D(n)-triple in Z[i] for two distinct n’s other than n= – 1 and these triples are not equivalent to any triple with the property D(1).